Question

are these triangles similar?
yes
no

Explanation:

Step1: Calculate the third angle of triangle DEF

The sum of angles in a triangle is \(180^{\circ}\). For \(\triangle DEF\), if two angles are \(35^{\circ}\) and \(55^{\circ}\), then the third angle \(\angle F=180^{\circ}-(35^{\circ} + 55^{\circ})=180^{\circ}-90^{\circ} = 90^{\circ}\)

Step2: Calculate the third angle of triangle HIG

For \(\triangle HIG\), if two angles are \(81^{\circ}\) and \(55^{\circ}\), then the third angle \(\angle H=180^{\circ}-(81^{\circ}+55^{\circ})=180^{\circ} - 136^{\circ}=44^{\circ}\)

Step3: Check for similarity

Similar triangles have equal corresponding angles. The angles of \(\triangle DEF\) are \(35^{\circ},55^{\circ},90^{\circ}\) and the angles of \(\triangle HIG\) are \(81^{\circ},55^{\circ},44^{\circ}\). Since the sets of angles are not equal, the triangles are not similar.

Answer:

No